Global dynamical behaviors for an sir epidemic model with time delay and pulse vaccination

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	Global dynamical behaviors for an sir epidemic model with time delay and pulse vaccination
	Meng, Xinzhu 1; Chen, Lansun 2
	2008-08-01
发表期刊	TAIWANESE JOURNAL OF MATHEMATICS
ISSN	1027-5487
卷号	12 期号:5 页码:1107-1122
摘要	Since the investigation of impulsive delay differential equations are inchoate, the literature on delay epidemic models with pulse vaccination is not extensive. In this paper, we propose a delay SIR epidemic model with impulsive effect and analyze the global dynamics behaviors of the model. Using the discrete dynamical system determined by the stroboscopic map, we show that there exists an 'infection-free' periodic solution in the model. Further, we prove that the 'infection-free' periodic solution is globally attractive when the period of impulsive effect is less than some critical value. The condition for the permanence of population for epidemic model with pulse vaccination is given, which means the epidemic disease to spread around. We conclude that time delay and pulse bring great effects on the dynamics of the model. It illustrated theoretically that we should look carefully after the infectious patients to shorten the convalescence period (or infections period). Lastly, the biologic discussion and strategy for the elimination of infectious diseases are also given. In this paper, the main feature is that we introduce time delay together with pulse into epidemic model, and we investigate their effects on the dynamics of model.
关键词	permanence pulse vaccination horizontal and vertical transmission time delay global attractivity
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000258111700008
出版者	MATHEMATICAL SOC REP CHINA
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5823
专题	中国科学院数学与系统科学研究院
通讯作者	Meng, Xinzhu
作者单位	1.Shandong Univ Sci & Technol, Coll Sci, Qingdao 266510, Peoples R China 2.Acad Sinica, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Meng, Xinzhu,Chen, Lansun. Global dynamical behaviors for an sir epidemic model with time delay and pulse vaccination[J]. TAIWANESE JOURNAL OF MATHEMATICS,2008,12(5):1107-1122.
APA	Meng, Xinzhu,&Chen, Lansun.(2008).Global dynamical behaviors for an sir epidemic model with time delay and pulse vaccination.TAIWANESE JOURNAL OF MATHEMATICS,12(5),1107-1122.
MLA	Meng, Xinzhu,et al."Global dynamical behaviors for an sir epidemic model with time delay and pulse vaccination".TAIWANESE JOURNAL OF MATHEMATICS 12.5(2008):1107-1122.